Question

what is the magnitude of the resultant of a 100-newton force along the x-axis and a 150-new2ton force at an angle of 40 degrees to each other

Answer 1

235.54 N

Explanation:

Since this is an addition of vectors, we need to find the components of each in the x-y plane. Given that the first vector (100 N) is along the x axis, it consist of just x component of size: 100N.

For the second vector, its x-component will be given by the cosine projection on the x axis via:

x-component
`=150*cos(40^o)=114.9`

and its y-component will be given by the "sine" projection:

y component
`=150*sin(40)=96.42`

Therefore the addition of the x-components for the final vector is:

100N + 114.9N = 214.9 N

Now we use the Pythagorean theorem to find the magnitude of the resultant addition of vectors:

`√(96.42^2+214.9^2) =√(55478.8264) =235.54 N`